Solve for $x$ and $y$ by deriving an expression for $y$ from the second equation, and substituting it back into the first equation. $\begin{align*}-6x+6y &= -6 \\ 7x-5y &= -3\end{align*}$
Begin by moving the $x$ -term in the second equation to the right side of the equation. $-5y = -7x-3$ Divide both sides by $-5$ to isolate $y$ $y = {\dfrac{7}{5}x + \dfrac{3}{5}}$ Substitute this expression for $y$ in the first equation. $-6x+6({\dfrac{7}{5}x + \dfrac{3}{5}}) = -6$ $-6x + \dfrac{42}{5}x + \dfrac{18}{5} = -6$ Simplify by combining terms, then solve for $x$ $\dfrac{12}{5}x + \dfrac{18}{5} = -6$ $\dfrac{12}{5}x = -\dfrac{48}{5}$ $x = -4$ Substitute $-4$ for $x$ back into the top equation. $-6( -4)+6y = -6$ $24+6y = -6$ $6y = -30$ $y = -5$ The solution is $\enspace x = -4, \enspace y = -5$.